Section 2.3, due on Sept 2

1. The most difficult part of this reading was the Theorems. I didnt quite understand what exactly the Fundamental Principle of Arithmetic was saying. I couldn't understand the proof cause I didt know what was being proved. Other theorems that were challenging for me to understand was Theorem 2.3.2 and 2.3.4. What is a UFD? how does it apply to F[x] in Thm 2.3.5?

2. The only part of this section that I understood was Lemma 2.3.1, Euclid's Lemma, and Corollary 2.3.1.

Sections 2.1 and 2.2, due on Sept 1

1. I still have trouble reading the mathematical language, for example, reading proofs and theorems and definitions. In 2.2 Definition 2.2.1 where it talks about how divisibility is denoted and how it will be referred to throughout the book initially gives me trouble understanding it. The notation could sometimes be a bit confusing, but I know that it is a very vital part of this class and that it will take much practice.

2. The part I enjoyed most about the reading was the review of rings, commutative rings, integral domains even though I'm still a bit "iffy" on integral domains, It was nice to be able to review material from Abstract Algebra. Since Math 290 (190 as it was called when I took it) Proof by Mathematical Induction has really come to my understanding significantly! Its always nice to see material over again to solidify it in my mind.

Introduction, due on Sept 1

1. What was the most difficult part of the section for me?

To be frank the most difficult part of the section of reading was trying to stay awake. Not that it was that boring, but that I have been lacking sleep the past week. However, concerning the material covered in the introduction I believe the most difficult part for me was trying to imagine what is being covered. For example, "Mathematically it is just an infinite cyclic group" (p.1) I was trying to imagine how that could look like on a number line. What element generates all the integers? was even just talking about the integers? or the real numbers, the rational numbers, the irrational numbers, the complex numbers, etc. ?
Another part of the introduction that was a difficult for me was the some of the work that was described in the history that is there. Dirichlet using analytic methods, that there are infinite primes in any arithmetic progression {a+nb} with a,b relatively prime. I could grasp an understanding of it but the mathematical language is still a bit mind boggling for me. I have read it a few times before I can grasp it.

2. I did however enjoy the history part of the section. Reading about how "Number theory arises from arithmetic and computation with whole numbers" Also about the applications of it in every culture. I always knew that our number system came from the Arabic number system, however,I never knew the official name to be "Hindu-Arabic numeration system" and was developed in India!